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Published byJorge Joel Modified about 1 year ago

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Project Management - Part 2

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Overview What happens when activity times in a project are: Not fixed Crashing the project Not known with certainty PERT (Project Evaluation and Review Technique)

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Project Crashing Estimated time is fixed... no more. Can reduce the length of time of a project through additional resources manpower, equipment Direct cost of activity is always increased

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Project Crashing: Motivation Need to reduce time of project because: Requirement to complete in specified time frame Economic advantage Three kinds of costs Crash costs (activity direct costs) Administration costs (or project indirect costs) Penalty costs Incur crash costs to avoid administration and penalty costs

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Calculating Crash Costs per Unit Time Crash Time =3 Normal Time =7 Crash Cost = $9,000 Normal Cost = $3,000 Crash Cost / Unit Time = 9000 – – 3 = $1,500

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Project Crashing: Procedure Always crash one period at a time! 1.Identify critical activities 2.Select least expensive to crash 3.Savings? Implement if so. Update all paths 4.Repeat 1-3 until no cost savings are possible

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21 53 A B CD XY Z ABCD AXYZ Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 Normal Duration: Minimum Duration: Path Duration Which activity should we crash? (per period)

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ABCD 16 AXYZ 15 Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration (per period)

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ABCD 16 AXYZ 15 Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration (per period)

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ABCD 16 AXYZ 15 Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration (per period)

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A B CD XY Z ABCD 16 AXYZ 15 Choose B because it is the cheapest of the three alternatives (A, B, or C) Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration B (per period)

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A B CD XY Z ABCD AXYZ B Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration Cost Save Net Cumul Which activity(s) should we crash next? (per period)

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A B CD XY Z ABCD AXYZ Cost 100 Save 500 Net 400 Cumul 400 B Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration (per period)

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A B CD XY Z ABCD AXYZ Cost 100 Save 500 Net 400 Cumul 400 B Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration (per period)

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A B CD XY Z ABCD AXYZ Cost 100 Save 500 Net 400 Cumul 400 B Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration (per period)

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A B CD XY Z ABCD AXYZ Cost 100 Save 500 Net 400 Cumul 400 B Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration (per period)

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A B CD XY Z ABCD AXYZ Cost 100 Save 500 Net 400 Cumul 400 B Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration (per period)

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A B CD XY Z ABCD AXYZ Cost 100 Save 500 Net 400 Cumul 400 B Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration (per period)

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A B CD XY Z ABCD AXYZ Cost 100 Save 500 Net 400 Cumul 400 B Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration (per period)

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A B CD XY Z ABCD AXYZ Cost 100 Save 500 Net 400 Cumul 400 B Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration BY (per period)

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A B CD XY Z ABCD AXYZ Cost Save Net Cumul B BY Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration Which activity(s) should we crash next? (per period)

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A B CD XY Z ABCD AXYZ Cost Save Net Cumul B BY Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration (per period)

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A B CD XY Z ABCD AXYZ Cost Save Net Cumul B BY Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration (per period)

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A B CD XY Z ABCD AXYZ Cost Save Net Cumul B BY Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration (per period)

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A B CD XY Z ABCD AXYZ Cost Save Net Cumul B BY Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration (per period)

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A B CD XY Z ABCD AXYZ Cost Save Net Cumul Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration B BY A (per period)

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A B CD XY Z ABCD AXYZ Cost Save Net Cumul B BY A Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration (per period)

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A B CD XY Z ABCD AXYZ Cost Save Net Cumul B BY A Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration Which activity(s) should we crash next? (per period)

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A B CD XY Z ABCD AXYZ Cost Save Net Cumul B BY A CY Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration (per period)

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A B CD XY Z ABCD AXYZ Cost Save Net Cumul B BY A CY Crash Costs A -$250 B-$100 C-$200 D- X-$350 Y-$125 Z-$325 Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration Which activity(s) should we crash next? (per period)

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A B CD XY Z ABCD AXYZ Cost Save Net Cumul B BY A CY CZ We lose $$, so do not crash CZ Admin Cost = $500 A B CD XY Z Normal Duration: Minimum Duration: Path Duration

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A B CD XY Z ABCD AXYZ Cost Save Net Cumul B BY A CY A B CD XY Z Normal Duration: Minimum Duration: Path Duration Most economical duration Achieved by crashing Spent $900 in increased direct costs Avoided $2000 in administration costs Net savings

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PERT (CPM With 3 Time Estimates) In past, time estimate is firm Now… task duration is uncertain New activity Natural variance Use 3 time estimates to deal with uncertainty a = most optimistic estimate m = most likely b = most pessimistic

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Formulas e t (expected time) = (a + 4m + b)/6 σ (standard dev) = (b - a)/6 σ 2 (variance) = (b - a) 2 /36 = [(b - a)/6] 2 Z = (D - e t )/σ How many standard deviations away D is from e t

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Activity List for Example Problem Activity Description Immediate Predecessors Required Activity Time (weeks) A B C D E F G H I J Select office site Create organization and financial plan Determine personnel requirements Design facility Construct the interior Select personnel to move Hire new employees Move records, key personnel, etc. Make financial arrangements Train new personnel - - B A,C D C F F B H,E,G

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Mean and Variance Activity a m b ET óó 2 A B C D E F G H I J /3 1 1/3 2/3 2 5/6 1/3 1/2 4/9 1 1/9 4/9 4 25/36 1/9 1/4 e t = (a + 4m + b)/6 σ = (b - a)/6 σ 2 = (b - a) 2 /36 = [(b - a)/6] 2 (1+4·3+5)/6 (5-1)/6 [(5-1)/6] 2 e t = = = For activity A, etet

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Path Length Path length is the sum of expected times of activities on the path not sum of most likely times Longest expected path length is critical Path length is uncertain, and so is project duration Path has variance equal to sum of variances of individual activities on path

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A B D C E F G H I J

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A B D C E F G H I J

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e t = If we want to know the probability of completing the project in 22 weeks or less: Calculating probability of different completion time

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Calculations e t = 23 weeks σ 2 CP = 2 BCDEJ Z = (D - e t )/ σ CP = (22-23)/ = Take.42 to the Z table => =.34 Beware - never add standard deviations! = = σ 2 B + σ 2 C + σ 2 D + σ 2 E + σ 2 J

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22 is 0.42 SD below Mean of e t = % chance < 22 (table) 50% chance > 23 16% chance between 22 and 23

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